Relaxation approximation of the Euler equations

Chalons, Christophe; Coulombel, Jean-François

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jmaa.2008.07.034

Title :

Relaxation approximation of the Euler equations

Author(s) :

Chalons, Christophe [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Coulombel, Jean-François [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Journal of Mathematical Analysis and Applications

Pages :

872 - 893

Publisher :

Elsevier

Publication date :

2008-12

ISSN :

0022-247X

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

The aim of this paper is to show how solutions to the one-dimensional compressible Euler equations can be approximated by solutions to an enlarged hyperbolic system with a strong relaxation term. The enlarged hyperbolic ...
Show more >The aim of this paper is to show how solutions to the one-dimensional compressible Euler equations can be approximated by solutions to an enlarged hyperbolic system with a strong relaxation term. The enlarged hyperbolic system is linearly degenerate and is therefore suitable to build an efficient approximate Riemann solver. From a theoretical point of view, the convergence of solutions to the enlarged system towards solutions to the Euler equations is proved for local in time smooth solutions. We also show that arbitrarily large shock waves for the Euler equations admit smooth shock profiles for the enlarged relaxation system. In the end, we illustrate these results of convergence by proposing a numerical procedure to solve the enlarged hyperbolic system. We test it on various cases.Show less >

Language :

Anglais

Popular science :

Non

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